If I notice that a connection on an object is, for example, on the wrong layer, but I already have 20 of them  on a drawing, can I go edit the symbol, save it, then refresh the drawing so the objects display the new change??

No - editing a symbol file does not change anything in an existing drawing; they are distinct and unrelated files. However, you can select multiple objects in a drawing and set them to a new layer by sleecting that layer from the Layers dropdown box.

Kind regards,
Rob Robinson
Stardraw.com